Rate for harmonic Frank–Wolfe on general polytopes

Determine convergence-rate estimates for the direct harmonic Frank–Wolfe recursion applied to monotone variational inequalities on general compact polytopes, without imposing strong convexity of the feasible set.

Background

The paper discusses the direct harmonic Frank–Wolfe recursion for variational inequalities on polytopes. Existing convergence results for monotone operators on compact convex sets provide asymptotic convergence, but the associated rate estimates require additional geometric regularity, specifically strong convexity of the feasible set.

The paper resolves an affine, strongly monotone case on polytopes when the solution lies in the relative interior, obtaining an $O(k^{-1})$ last-iterate norm bound. It explicitly leaves the rate question for general polytopes unresolved.